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Superhydrophobicity and self-cleaning require a combination of surface topography and low-energy surfaces, where mechanical damage of the topography or contamination with oils lead to loss of the nonwetting properties. We show that such vulnerability can be solved by superamphiphobic (i.e., both superhydrophobic and superoleophobic) surfactant-coated aerogel surfaces. Using silica aerogels as model materials, the self-similar network structure allows fresh re-entrant surface topographies even after removal of the uppermost layer upon mechanical abrasion, and superoleophobicity suppresses oil contamination. Given the recent progress toward mechanically strong aerogels, we foresee that the concept can open routes for robust self-cleaning coating technologies.